Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of #92150⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #92150⋊C2 |
| unambiguous semidirect product | D112⋊C2 |
| Fitting, socle, Sylow | C112 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C11⋊D11 | C22 |
| Fitting, socle, hypocenter | C112 | D4 |
| LCS | G ▷ C11⋊D11 ▷ C112 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22 |
Polycyclic presentation:
2^3,11^2|b^a=bc,d^a=d^10,d^b=e,e^b=d,d^c=d^10,e^c=e^1035 conjugacy classes — view the full character table.
| maximal subgroup of | #11757261⋊C2, C2×#92150⋊C2, #72224479, … |
| maximal normal subgroup of | #11757261⋊C2, C2×#92150⋊C2, #72224481 |
| maximal quotient of | D112⋊C4, #14515511, #14515512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 36);